Abstract
In this paper, we propose heuristics for solving the survivable network design problem(SNDP) which is known to be NP-hard. In the SNDP, we want to obtain a minimum cost network design that satisfies survivability constraints given by the number of node-disjoint paths for each pair of nodes of a given graph. For solving the SNDP, we propose 2 heuristics that use a local search method with search space smoothing. The search space smoothing generates a series of smoothed search spaces that approximate the original search space. The smoothed search space has fewer local minima than the original search space and if we solve the problem with the smoothed search space, we can easily approach to the global minimum of the original problem. The results of computational experiments show the efficiency of the proposed heuristics.
Hyundai Electronics Industries Co., LTD.,Korea
Kyung Hee University, Korea
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References
R. H. Cardwell, C. L. Monma, and T. H. Wu, Computer-Aided Design Procedures for Survivable Fiber Optic Networks, IEEE Journal on Selected Areas in Communication, Vol. 7, No. 8, pp. 1188–1197, 1989
M. X. Goemans and D. J. Bertsimas, Survivable Networks, Linear Programming Relaxations and the Parsimonious Property, Mathematical Programming, Vol. 60, pp. 145–166, 1993
M. Grötschel and C. L. Monma, Integer Polyhedra Arising from Certain Network Design Problems with Connectivity Constraints, SI AM J. Disc. Math., Vol. 3, No.4, pp. 502–523, 1990
M. Grötschel, C. L. Monma, and M. Store, Computational Results with a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints, Operations Research, Vol.40, No.2, pp.309–330, 1992
M. Grötschel, C. L. Monma, and M. Store, Polyhedral and Computational Investigations for Designing Communication Networks with High Survivability Requirements, Operations Research, Vol.43, No.6, pp.1012–1024, 1995
J. Gu and X. Huang, Efficient Local Search with Search Space Smoothing: a Case Study of the Traveling Salesman Problem(TSP), IEEE Transactions on Systems, Man, and Cybernetics, Vol. 24, No. 5, pp.728–734, 1994
J. Gu, Optimization by Multispace Search, Technical Report, Dept. of Electrical and Computer Engineering, Univ. of Calgary, UCECE-TR-90-001, Jan. 1990
J. Gu, Optimization by Multispace Search, Kluwer Academic Publishers, Massachusetts, 1996
J. Gu, Multispace Search: A New Optimization Approach (Summary), Lecture Notes in Computer Science, Vol. 834, Ding-Zhu Du, pp. 252–260, 1994
J. Gu and B. Du, A Multispace Search Algorithm for Molecular Energy Minimization, DIM ACS Volume Series on Discrete Mathematics and Theoretical Computer Science, Vol. 23, Editors: Panos Pardalos, Shalloway, and G.L. Xue, American Mathematical Society, pp. 65–87, 1995
C.-G. Han et al., Survivable Network Design Problems with Given Conduits, Korean Information Science Society Proceeding, Vol.22, No.l, pp.618–621, 1995
C. L. Monma and D. F. Shallcross, Methods for Designing Communication Networks with Certain Two-Connected Survivability Constraints, Operations Research, Vol. 37, pp. 531–541, 1989
K. Steiglitz, P. Weiner, and D. J. Kleitman, The Design of Minimum-Cost Survivable Networks, IEEE Transaction on Circuit Theory, Vol.ct-16, No.4, pp.455–460, 1969
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© 1997 Springer-Verlag Berlin Heidelberg
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Park, JC., Han, CG. (1997). Solving the Survivable Network Design Problem with Search Space Smoothing. In: Pardalos, P.M., Hearn, D.W., Hager, W.W. (eds) Network Optimization. Lecture Notes in Economics and Mathematical Systems, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59179-2_19
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DOI: https://doi.org/10.1007/978-3-642-59179-2_19
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